Answer:
The pathway will be 3 meters wide
Step-by-step explanation:
Let
x ----> the width of the pathway
we know that
The area of the pathway is equal to the area of the garden plus the pathway minus the area of the garden
The area of the pathway must be equal to 336 square meters
so
the linear equation that represent this situation is
[tex](2x+30)(2x+20)-(30)(20)=336[/tex]
solve for x
[tex]4x^2+40x+60x+600-600=336[/tex]
[tex]4x^2+100x=336[/tex]
[tex]4x^2+100x-336=0[/tex]
Simplify the quadratic equation (Divide by 4 both sides)
[tex]x^2+25x-84=0[/tex]
Solve the quadratic equation by graphing
using a graphing tool
The solution is x=3 m
see the attached figure
therefore
The pathway will be 3 meters wide
